Some results on strong convergence for nonlinear maps in Banach spaces

Volume 10, Issue 5, pp 2828--2836 http://dx.doi.org/10.22436/jnsa.010.05.48

Publication Date: May 25, 2017 Submission Date: February 19, 2017

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Authors

Abdul Latif - Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah-21589, Saudi Arabia. Adnan Salem Alhomaidan - Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah-21589, Saudi Arabia. Xiaolong Qin - Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Sichuan, China.

Abstract

In this paper, an equilibrium problem which is also known as the Ky Fan inequality is investigated based on a fixed point method. Strong convergence theorems for solutions of the equilibrium problem are established in the framework of reflexive Banach spaces. Applications are also provided to support the main results.

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Keywords

• Equilibrium problem
• fixed point
• nonexpansive mapping
• variational inequality
• hybrid method.

MSC

•  47H09
•  47N10
•  90C30

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